login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A057624 Initial prime in first sequence of n primes congruent to 1 modulo 4. 6
5, 13, 89, 389, 2593, 11593, 11593, 11593, 11593, 373649, 766261, 3358169, 12204889, 12270077, 12270077, 12270077, 297387757, 297779117, 297779117, 1113443017, 1113443017, 1113443017, 1113443017, 1113443017, 84676452781, 84676452781, 689101181569, 689101181569, 689101181569, 3278744415797, 3278744415797, 3278744415797, 3278744415797 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The sequence is infinite, by Shiu's theorem. - Jonathan Sondow, Jun 22 2017
REFERENCES
R. K. Guy, Unsolved Problems in Number Theory, A4.
David Wells, The Penguin Dictionary of Curious and Interesting Numbers, Revised Edition, Penguin Books, London, England, 1997, page 163.
LINKS
D. K. L. Shiu, Strings of Congruent Primes, J. Lond. Math. Soc. 61 (2) (2000) 359-373 [MR1760689]
EXAMPLE
a(9) = 11593 because "[t]his number is the first in a sequence of 9 consecutive primes all of the form 4n + 1."
MATHEMATICA
NextPrime[ n_Integer ] := Module[ {k = n + 1}, While[ ! PrimeQ[ k ], k++ ]; Return[ k ] ]; PrevPrime[ n_Integer ] := Module[ {k = n - 1}, While[ ! PrimeQ[ k ], k-- ]; Return[ k ] ]; p = 0; Do[ a = Table[ -1, {n} ]; k = Max[ 1, p ]; While[ Union[ a ] != {1}, k = NextPrime[ k ]; a = Take[ AppendTo[ a, Mod[ k, 4 ] ], -n ] ]; p = NestList[ PrevPrime, k, n ]; Print[ p[ [ -2 ] ] ]; p = p[ [ -1 ] ], {n, 1, 19} ]
CROSSREFS
Sequence in context: A263468 A350467 A081560 * A092567 A055623 A280294
KEYWORD
nonn
AUTHOR
Robert G. Wilson v, Oct 09 2000
EXTENSIONS
More terms from Don Reble, Nov 16 2003
More terms from Jens Kruse Andersen, May 29 2006
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 19 09:19 EDT 2024. Contains 371782 sequences. (Running on oeis4.)